timesync: fix parsing FallbackNTP= (#40692)

Follow-up for 3745770ae4.
Fixes #40621.

src/timesync/test-timesync.c

@@ -15,9 +15,9 @@ TEST(manager_parse_string) {
 
         assert_se(manager_new(&m) == 0);
 
-        assert_se(!m->have_fallbacks);
+        assert_se(!m->fallback_set);
         assert_se(manager_parse_server_string(m, SERVER_FALLBACK, NTP_SERVERS) == 0);
-        assert_se(m->have_fallbacks);
+        assert_se(m->fallback_set);
         assert_se(manager_parse_fallback_string(m, NTP_SERVERS) == 0);
 
         assert_se(manager_parse_server_string(m, SERVER_SYSTEM, "time1.foobar.com time2.foobar.com axrfav.,avf..ra 12345..123") == 0);

src/timesync/timesyncd-conf.c

@@ -20,7 +20,7 @@ int manager_parse_server_string(Manager *m, ServerType type, const char *string)
         first = type == SERVER_FALLBACK ? m->fallback_servers : m->system_servers;
 
         if (type == SERVER_FALLBACK)
-                 m->have_fallbacks = true;
+                 m->fallback_set = true;
 
         for (;;) {
                 _cleanup_free_ char *word = NULL;
@@ -59,7 +59,7 @@ int manager_parse_server_string(Manager *m, ServerType type, const char *string)
 }
 
 int manager_parse_fallback_string(Manager *m, const char *string) {
-        if (m->have_fallbacks)
+        if (m->fallback_set)
                 return 0;
 
         return manager_parse_server_string(m, SERVER_FALLBACK, string);
@@ -84,15 +84,21 @@ int config_parse_servers(
         assert(lvalue);
         assert(rvalue);
 
-        if (isempty(rvalue))
+        if (isempty(rvalue)) {
                 manager_flush_server_names(m, ltype);
-        else {
-                r = manager_parse_server_string(m, ltype, rvalue);
-                if (r < 0) {
-                        log_syntax(unit, LOG_WARNING, filename, line, r,
-                                   "Failed to parse NTP server string '%s', ignoring: %m", rvalue);
-                        return 0;
-                }
+
+                /* FallbackNTP= with an empty string disables the built-in fallback servers. */
+                if (ltype == SERVER_FALLBACK)
+                        m->fallback_set = true;
+
+                return 0;
+        }
+
+        r = manager_parse_server_string(m, ltype, rvalue);
+        if (r < 0) {
+                log_syntax(unit, LOG_WARNING, filename, line, r,
+                           "Failed to parse NTP server string '%s', ignoring: %m", rvalue);
+                return 0;
         }
 
         return 0;

src/timesync/timesyncd-manager.h

@@ -33,7 +33,7 @@ typedef struct Manager {
 
         RateLimit ratelimit;
         bool exhausted_servers;
-        bool have_fallbacks;
+        bool fallback_set; /* Indicate if FallbackNTP= is explicitly configured. */
 
         /* network */
         sd_event_source *network_event_source;